For a differential field \((K,\partial )\) , the ring of differential operators \(\mathcal {D}=K[\partial ]\)  admits Euclidean division. For instance in [1]} \(K\)  is the field of fractions of the ring \({\bf C}[[x]]\)  or \({\bf C}\lbrace x \rbrace  \) . Given \(L\) , \(M\)  in \(\mathcal {D}\) , if \(\operatorname{ord}(M)\ge \operatorname{ord}(L)\)  then \(M=qL+r\)  with \(\operatorname{ord}(r)<\operatorname{ord}(L)\) , \(q,r\in K[\partial ]\) . Let us denote by \(\gcd (L,M)\)  the greatest common (right) divisor of \(L\)  and \(M\) .
